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This study focuses on the development of efficient algorithms for multiple marine vessel path planning considering dynamics, mission parameters, and external influences. The Go-To Formation Maneuver is discussed, emphasizing the need for concerted vehicle driving and collision avoidance. The path planning foundations, including polynomial path planning and cost function considerations, are explored. The study also delves into spatial and temporal deconfliction, incorporating environmental constraints using barrier functions. Simulation results showcase the algorithm's utilization of currents to minimize energy usage. Time-coordinated path following control strategies are proposed, ensuring trajectory tracking in the presence of disturbances. The study concludes with the planner's advancements in addressing currents and communication constraints, enhancing mission planning usability. The barrier function approach aids in probing path limits, crucial for obstacle avoidance.
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Multiple Marine Vehile Deconflicted Path Planning with Currents and Communication Constraints A. Häusler1, R. Ghabcheloo2, A. Pascoal1, A. Aguiar1 1Instituto Superior Técnico, Lisbon, Portugal 2Tampere University of Technology, Tampere, Finland
Introduction • Efficient algorithms for multiple vehicle path planning are crucial for cooperative control systems • Need to take into account vehicle dynamics, mission parameters and external influences • Example: Go-To-Formation maneouvre Andreas J. Häusler - IAV 2010
The Go-To-Formation Maneouvre Current Mother Ship • An initial formation pattern must be established before mission start • Deploying the vehicles cannot be done in formation (no hovering capabilities) • Vehicles can’t be driven to target positions separately (no hovering capabilities) Andreas J. Häusler - IAV 2010
The Go-To-Formation Maneouvre Mother Ship • Need to drive the vehicles to the initial formation in a concerted manner • Ensure simultaneous arrival times and equal speeds • Establish collision avoidance through maintaining a spatial clearance Andreas J. Häusler - IAV 2010
Path Planning Foundations Final position Initial position Andreas J. Häusler - IAV 2010
Polynomial Path Planning • Dispense with absolute time in planning a path (Yakimenko) • Establish timing laws describing the evolution of nominal speed with • Spatial and temporal constraints are thereby decoupled and captured by & • Choose and as polynomials • Path shape changes with only varying Andreas J. Häusler - IAV 2010
Polynomial Path Planning • Polynomial for each coordinate with degree determined by the number of boundary conditions • Temporal speed and acceleration constraints • Choice for timing law with Andreas J. Häusler - IAV 2010
CostFunctionConsiderations Andreas J. Häusler - IAV 2010
Cost Function Considerations • A path is feasible if it can be tracked by a vehicle without exceeding , , and • It can be obtained by minimizing the energy consumption • subject to temporal speed and acceleration constraints Andreas J. Häusler - IAV 2010
Multiple Vehicle Path Planning • Instead of trying to minimize the arrival time interval, we can fix arrival times to be exactly equal and still get different path shapes • Integrate for Andreas J. Häusler - IAV 2010
Multiple Vehicle Path Planning • Then we obtain , from which the spatial paths are computed • The result is in turn used to compute velocity and acceleration • Optimization is done using direct search Andreas J. Häusler - IAV 2010
Spatial Deconfliction Final positions (target formation) Initial positions Andreas J. Häusler - IAV 2010
Temporal Deconfliction Final positions (target formation) Initial positions Andreas J. Häusler - IAV 2010
Deconfliction • Spatial deconfliction: subject to • For temporal deconfliction, the constraint changes to • Simultaneous arrival at time Andreas J. Häusler - IAV 2010
Environmental Constraints • Incorporated throughbarrier function • Path planningwithcurrentsformoreenergy-efficientpaths (insteadofsolelyrelying on pathfollowingcontroller) • Path planningwithcommunicationconstraintsforrangekeepingwithinthegroup (Hauser, CDC 2006) Andreas J. Häusler - IAV 2010
Path Planning System MissionSpecifications SpatialClearance Optimization Algorithm Comm. Constraint CostCriterion PathGeneration InitialGuess AMV Data Init. Position & Heading Path Nominal Paths InitialVelocity Time-CoordinatedPathFollowing Final Position & Heading Revised Guess SpeedProfiles Final Velocity DynamicalConstraints EnvironmentalConstraints Current Obstacles Andreas J. Häusler - IAV 2010
Time-Coordinated Path Following • Closed-form solution to problems of open-loop path planning and trajectory tracking • Using virtual time with (Ghabcheloo, ACC 2009) Andreas J. Häusler - IAV 2010
Time-Coordinated Path Following • Path followingcontrolstrategy • Guaranteesthatvehiclesandaredeconflictedandthattheyfollowtheirtrajectoryif • A time coordinationcontrollawcanbefound so thatthemissionremains “near optimal“ in thepresenceofdisturbances Andreas J. Häusler - IAV 2010
Simulation Results • Algorithm makes use of currents to minimize expected energy usage • Solid lines = vw, dashed lines = vdes and dotted lines = vmin and vmax Andreas J. Häusler - IAV 2010
Simulation Results • Algorithm makes use of currents to minimize expected energy usage • Solid lines = vw, dashed lines = vdes and dotted lines = vmin and vmax Andreas J. Häusler - IAV 2010
Simulation Results • Communication constraints with and without spatial deconfliction • Communication break distance 50m and 80m Andreas J. Häusler - IAV 2010
Conclusions • Recent improvements of the planner include currents and communication constraints • Thereby enhances usability for mission planning • Barrier function approach allows for “probing” the path limits (useful for obstacle avoidance) • Algorithm easily adaptable for arbitrary number of vehicles Andreas J. Häusler - IAV 2010
Future Work • Running time increases exponentially with number of discrete points use different optimization approach and/or different means of path description • Incorporate real vehicle dynamics instead of approximation through constraints • Improve communication constraint • Use more sophisticated energy usage equation • Allow for specification of vehicle sub-groups Andreas J. Häusler - IAV 2010
Thank you for your attention! Outlook: trajectoryoptimizationusing a projectionoperatorapproach (blue: desiredpath, green: timeandenergyoptimalpathaccording to vehicledynamics Outlook: obstacleavoidanceusing the projectionoperator Outlook: collisionavoidanceusing the projectionoperator Outlook: obstacle and collision avoidance using a projection operatoroptimization approach Andreas J. Häusler - IAV 2010
